$59 a day in St. Louis will feed you pretty well in my opinion. On average, you can generally get a very good meal for $15-20.
I am not very aquainted with the restaurants in the immediate downtown. Although I lived about 4 miles south, we rarely went into the DT area for restaurants as the selection was not as good as some of the neighborhoods.
The restaurant at the Pavillion Hotel has always been fairly reliable and is centrally located at One South Broadway.
Heading up Market St. is the Union Station. The restaurants there are not great but you have to check out the building as well as the Drury Inn across the street.
There are several areas close to downtown that have pretty good food.
The closest is the Soulard area which is about two miles south of the DT area, There are a lot of trendy restaurants. However, I would not recommend walking as the area between Soulard and DT is pretty rough.
The second area is the Grand Ave area which is about four miles from town and features a number of Asian restaurants. One of the originals is The King and I for Thai which is pretty decent but not as good as you would get in Chicago. They are group friendly. Pho Grand is a very excellent Vietnamese place but their seating is fairly limited. The prices are very reasonable. Also, Mekong Delta serves up some pretty good Vietnamese but not as good as Pho Grand. You'll need a taxi to get there. Do NOT try the MetroLink train to Grand as the station is a distance away from the restaurants through an industrial area.
The third areas is The Hill. While I used to live very close to it, I could never get a firm answer as to where it starts and ends. They feature mostly Italian restaurants and you can search for specific recommendations. We really liked Favazzas on Southwest but my last couple of meals have not been that great. You will need a cab to get here.
The fourth area is 4 miles west of downtown - the Central Westend and is accessible from the MetroLink train from downtown. There are a number of restaaurants in the streets behind the Barnes-Children Medical Center. My favorite is the India Rasoi on Laclede. They offer a good variety of South Indian restaurants with vegetarian selections.
India's Rasoi
4569 Laclede Ave
St Louis, MO 63108-2103 View Map
(314) 361-6911
Also, the area is a pretty good walking area with a lot of street traffic.